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Winning Financial Trading with Equilibrium Fractal Wave Winning Financial Trading with Equilibrium Fractal Wave Subtitle: Introduction to Equilibrium Fractal Wave Trading Author: Young Ho Seo Finance Engineer and Quantitative Trader Book Version: 2.2 (16 October 2018) Publication Date: 13 February 2017 Total Pages counted in MS-Word: 121 Total Words counted in MS-Word: 14,500 [email protected] www.algotrading-investment.com About the book This book will introduce you the brand new concept called “Equilibrium fractal wave” for the financial trading. This powerful concept can guide and improve your practical trading. The concept taught here can also help the strategist to create new trading strategies for Stock and Forex market. Please note that this book was designed to introduce the equilibrium fractal wave concept mostly. If you are looking for more trading strategy oriented guidelines, then please read “Financial Trading with Five Regularities of Nature” instead of this book. You can find the Book “Financial Trading with Five Regularities of Nature”: Scientific Guide to Price Action and Pattern Trading (Seo, 2017) in both from amazon.com and algotrading-investment.com. 2 Risk Disclaimer The information in this book is for educational purposes only. Leveraged trading carries a high level of risk and is not suitable for all market participants. The leverage associated with trading can result in losses, which may exceed your initial investment. Consider your objectives and level of experience carefully before trading. If necessary, seek advice from a financial advisor. Important warning: If you find the figures and table numberings are mismatched in this book, please report it to: [email protected] 3 Table of Contents About the book ................................................................................................................................... 2 1. Equilibrium Fractal Wave in the Contemporary Science ................................................................ 5 1.1 Introduction to Equilibrium Fractal Wave ................................................................................ 5 1.2 Empirical Research on Equilibrium Fractal Wave ................................................................... 15 1.3 Analogical Reasoning to the Modified Quantum Physics ....................................................... 19 2. Introduction to Equilibrium Fractal Wave for Financial Trading................................................... 22 3. Five Characteristics of Equilibrium Fractal Wave .......................................................................... 25 4. Hurst Exponent and Equilibrium Fractal Wave Index for Financial Trading ................................. 44 5. Shape Ratio Trading and Equilibrium Fractal Wave Channel ........................................................ 61 5.1 Introduction to EFW Index for trading .................................................................................... 61 5.2 Trading with the shape ratio of equilibrium fractal wave ...................................................... 66 5.3 Introduction to Equilibrium Fractal Wave (EFW) Channel ...................................................... 71 5.4 Practical trading with Equilibrium Fractal Wave (EFW) Channel ............................................ 79 5.5 Superimposed Equilibrium Fractal Waves .............................................................................. 86 5.6 Superimposed Equilibrium Fractal Wave Channel .................................................................. 93 6. Revealing the Market Structure with the distribution of EFW Index ......................................... 102 7. Appendix ..................................................................................................................................... 107 8. References .................................................................................................................................. 113 4 1. Equilibrium Fractal Wave in the Contemporary Science 1.1 Introduction to Equilibrium Fractal Wave The concept of Equilibrium Fractal Wave was first introduced in the book: Financial Trading with Five Regularities of Nature: Scientific Guide to Price Action and Pattern Trading (Seo, 2017). At that time, the book was written for the pure motivation to identify the important market dynamics for financial traders. The concept of Equilibrium Fractal Wave was born by combining two scientific areas including time series and fractal analysis. The main propositions in the Equilibrium Fractal Wave include: 1. The separate or combined analysis of trend and Fractal wave is possible. 2. The repeating patterns in Equilibrium Fractal Wave are equivalent to the infinite number of distinctive cycles because the scale of the repeating pattern varies infinitely. 3. Equilibrium Fractal Wave is a superclass of all the periodic wave patterns we know. First, let us demonstrate the equilibrium fractal wave for readers. The easiest way to demonstrate the equilibrium fractal wave is through the pattern table presented in Figure 1-1 (Seo, 2017). Many applied researchers in time series and statistics will agree that patterns in the column 1, 2, 3 and 4, from first regularity to fourth regularity, are the mainly extracted features and patterns in their everyday research and operation. It is also agreeable that cyclic wave pattern can co-present with trend together. This concept is the main assumption behind 5 the classic decomposition theory in the time series analysis. In the time series pattern table created by Gardner in 1987 (Figure 1-2) represents this concept clearly. The first row in the pattern table (Figure 1-1) shows the data in which no trend or weak trend exists. The second, third and fourth rows shows the co- existence of trend and waves. Until now, many forecasting or industrial scientists use such concept to build forecasting models. Likewise, there are many applied software to create the forecasting or prediction model of this kind. Some example forecasting software with such modelling capability includes: 1. Stata (www.stata.com) 2. Eviews (www.eviews.com) 3. IBM SPSS (www.ibm.com/products/spss-statistics) 4. SAS (www.sas.com) 5. MatLab (www.mathworks.com) 6. And many others 6 Figure 1-1: Five Regularities and their sub price patterns with inclining trends. Each pattern can be referenced using their row and column number. For example, exponential trend pattern in the third row and first column can be referenced as Pattern (3, 1) in this table. 7 Figure 1-2: The original Gardner’s table to visualize the characteristics of different time series data (Gardner, 1987, p175). Gardner assumed the three components including randomness, trend and seasonality in this table. Now the fifth column in Figure 1-1 presents the equilibrium fractal wave. This is extended part from the original Gardner’s table (Figure 1-2). When we list the equilibrium fractal wave in the fifth column, we can see that the pattern table (Figure 1-1) shows a systematic pattern. From left column to right column, we 8 can see that the number of distinctive cycles in the data increases. For example, we can assume the pure trend does not have any periodic cycle. Therefore, number of the distinctive cycle is zero for pure trend series. Under the second and third columns, we can have one to several distinctive cycles depending on if the series follows daily, monthly, and yearly cycles. Under fourth column, we can have many more distinctive cycles outside daily, monthly and yearly cycles but the number of the cycles is finite. Fourier analysis or principal component method can be used to reveal the number of cycles for any series under column 4. From column 1 to column 4, you might be following this systemic pattern pretty well. However, you might question why equilibrium fractal wave in column 5 possesses such infinite number of distinctive cycles. This is indeed the right question to ask. To understand this, you have to understand the fractal wave first. A lot of research on fractal analysis was done by B. Mandelbrot (1924-2010). The Book: fractal geometry of nature (Kirkby, 1983) describes the nature of fractal geometries in scientific language. What is the difference between fractal wave and equilibrium fractal wave in this article? Fractal wave views a series as the subject of fractal analysis. Equilibrium Fractal wave views a series as the co- subject of fractal analysis and trend analysis. Hence, equilibrium fractal wave believes co-existence of trend and wave pattern in a single data series. The significance of equilibrium fractal wave is that we can model the trend and fractal wave in two separate steps or in one-step. Indeed, scientists use the two-step process to model the data in column 2, 3 and 4 in economic and financial research. For example, price series under column 4 can be modelled with trend in the first step. Then the reminding data can be 9 modelled using cycles in the second step. Likewise, for a data series under column 5, we can model a trend part first, then we can model a fractal wave patterns in separate steps. This explains the Proposition 1. This also imposes the fractal analysis under non-stationary condition when the trend component is strong in the data series. In this case, two-step modelling process might be advantageous. When the trend component is less dominating comparing to fractal wave component, the entire price series can be modelled using fractal analysis only. Proposition 1 states that the choice on the modelling process,
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